רש"י suggests that Pharaoh's astrologers told him that they had a vision that a savior would be born on a certain day (שמות א:כב & שמות א:טז). Assuming the “astrologers” had no real power of prediction, what cause the astrologers to make up such a declaration? What was their plan?

Again, my premise is that they had no real power of prediction. I understand one may have the possibility that they had some power of Astrology, but for the purposes of this question I am taking the premise that they had no magic powers.

Beyond our current knowledge of the way the world works, there are many Rishonim that hold astrology and magic are not real. They hold that people often used these things to trick people into following them or their religion. They held there is not basis to astrology, talking to the dead, bad signs or omens etc. I have been asked to provide a source, so I have included one below.

"All the above matters are falsehood and lies with which the original
idolaters deceived the gentile nations in order to lead them after
them. It is not fitting for the Jews who are wise sages to be drawn
into such emptiness, nor to consider that they have any value as
[implied by Numbers 23:23]: "No black magic can be found among Jacob,
or occult arts within Israel." Similarly, [Deuteronomy 18:14] states:
"These nations which you are driving out listen to astrologers and
diviners. This is not [what God... has granted] you."

Whoever believes in [occult arts] of this nature and, in his heart,
thinks that they are true and words of wisdom, but are forbidden by
the Torah, is foolish and feebleminded. He is considered like women
and children who have underdeveloped intellects.

The masters of wisdom and those of perfect knowledge know with clear
proof that all these crafts which the Torah forbade are not
reflections of wisdom, but rather, emptiness and vanity which
attracted the feebleminded and caused them to abandon all the paths of
truth. For these reasons, when the Torah warned against all these
empty matters, it advised [Deuteronomy 18:13]: "Be of perfect faith
with God, your Lord."

No real power of prediction or no supernatural or divine power of prediction? Most people have some power of prediction. I predict someone will read this. What if they were doing it based on the science of the times?
– Kinnard HockenhullJan 15 '13 at 12:00

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Do you have sources which hold that they had no real power of prediction? If not, what is the point of this question?
– ShragaJan 15 '13 at 15:26

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It seems to me that they believed their wizardry, whether or not it actually worked, as Pharaoh must have. Hence, it would appear that they received some sign that led them to that conclusion - perhaps a miracle. Not that they regularly had some mystic powers, but that HaShem actually performed a miracle to allow their little tricks to reveal a sign of an actual future event that caused them to be concerned.
– Seth JJan 15 '13 at 17:12

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@SethJ Hmm. Thank you for the thoughts. Why would they consider their wizardry to work if they saw that it didn't work. If Hashem did cause a miracle in this instance, how would they know that? Wouldn't they just consider it to be the same as previous tries. Furthermore, if in fact it was a miracle, shouldn't this be reported in the Torah? This is a very interesting area, with lots of questions.
– RCWJan 15 '13 at 18:56

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@Shraga With regard to your comments on thinking for oneself I understand your point.However, I think at times that approach can be taken to an extreme. We must always be careful to be grounded in Torah and our sources. They are the bedrock of our Mesorah. However, one has to be able to be Mechadesh as well. The Torah was given to Man to use his mind to understand it. See the Ibn Ezra on Shemot 20:2. He clearly articulates the need for thoughtful analysis and using ones own mind to understand an area. Certainly our first approach is to see what our Chachamim say, but then it is left to us.
– RCWJan 16 '13 at 22:00

2 Answers
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Assuming the “astrologers” had no real power of prediction, we must understand what their plan was. What cause the astrologers to make up such a declaration? Perhaps there are two possible explanations to the astrologers plan. One approach is to suggest that the astrologers were working together with Pharaoh to come up with a plan to undermine Bnei Yisroel. Their plan was to annihilate any hope Bnei Yisroel would have for a savior or leader to arise. They used the "science of the times" to predict a way to destroy their hope. It was a method of propaganda to deter the chance of a leader arising. Another approach might be that the astrologers were working independently from Pharaoh, and they were trying to address the needs of Pharaoh. They sensed a fear and anxiety in Pharaoh that a savior would arise. It is only natural that a leader personality might arise from an oppressed people. The astrologers wanted to create a way to assuage Pharaoh's fear by presenting a vision of a savior that allows Pharaoh to act on this vision and address his fear. By believing that he could prevent the savior from coming it would calm his concerns.
This plan also seemed to get the support of the Egyptian people. Perhaps because the Egyptian's themselves were disgusted by the fact that the Bnei Yisroel continued to multiply. (See Shemot 1:12 and commentaries on the verse) This reminded them of the Bnei Yisroel’s power and how they had a powerful God that was with them. By attacking this very issue and killing the babies it allowed the Egyptians to feel relieved.

If you're assuming no astrology, magic, or other forms of mysticism, then one should look at political / sociological reasonings, with a historical context.

Pharoah is known to relieve his advisors, if and when he believes they are of no use to him (often "relieving" them of their heads - see e.g. the story of Yosef...)
Naturally, his advisors are opposed to this situation, and are constantly trying to prove their worth to The Great and Powerful Pharoah. They of course know that he doesn't have mystical powers, but that he tries to present himself as such.

Therefore, it would be easy to show how much he "needs" them - if he kills off all the babies born that day because of their "prediction", they have saved his life and kingdom! If it happens anyway - well, then its moot. If he decides to do nothing based on their prediction - well nothing ventured, nothing gained... but they knew he would do something. Besides, it is a well-worn trick to then "change" their prediction based on something else.

The real question about this, though, is why be so specific? Their philosophical descendants, all those palm-readers, fortune-tellers, and other mystics, have learned to be overly vague, allowing the mark customer to understand from it anything he wants, and allow for plausible deniability when it is not shown to be accurate.
On the other hand, Pharoah's astrologers do not have the lessons and experience of centuries of charlatanism to learn from. It is possible that they didn't figure that out, even though it seems so obvious to us now.